Optical tomography reconstruction algorithm based on the radiative transfer equation considering refractive index—Part 1: Forward model

The present study consists of two parts. The overall goal is to introduce and experimentally test the optical tomographic imaging algorithm based on the radiative transfer equation considering the refractive index. Considering that the high scattering medium with void-like regions has very low absorption and scattering coefficients, we use the radiative transfer equation to describe the optical parameters of the medium. In the process of photo propagation, not only the absorption and scattering coefficients have impact on the light radiance, but also the refractive index affect the light radiance. Therefore, we focus on the impact of the refractive index in this present study. We divide the refractive index into two cases: the uniform refractive index and the gradient refractive index.The paper is the first part of the present study, namely the forward model. We calculate the derivative of the fluency with the optical parameters by upwind-difference method, and a simpler mathematical framework is obtained in our study.In order to verify the accuracy of the forward model, we select the human brain phantom image with a void-like region and tumor as the experimental data. We found that the experimental measurements are in good agreement with the theoretical predictions of the measurements.